Advanced Placement (AP) Middle School

Marlene is solving a number puzzle involving three rational numbers a, b, and c. Here are her clues:
The quotient of a and c is 8.
The product of a and c is 2.
The quotient of a and b is -16.
The product of a and b is -1.
The quotient of b and c is -0.5.

Answers

Answer 1
Answer: a = 4, b = - 0.25, c = 0.5

8 is the quotient of either a/c or c/a. Additionally, ac = 2. Therefore either a or c must be 0.5, while the other is 4. This is because 4/0.5 = 8; 4 x 0.5 = 2.

-16 is the quotient of either a/b or b/a. At the same time, ab = -1. Due to this a cannot be 0.5, which would make b -8. If b is -8, then -8 x 0.5 does not equal -1. a must be 4. If a is 4, then c is 0.5. Solve for b, and you will find it is -0.25 (4/-0.25) = -16.

As a final proof, do the final step. The quotient of b/c is -0.5. -0.25/0.5 is in fact -0.5.
Answer 2

Answer:

So I got the same answers a=4, b=0.25, c=0.5

Explanation:

So first you have to go into the decimals because clearly no whole number can give you anything divined to get eight and multiplied to get two. So you can break it down and go into 1/2 because it’s the easiest way to start. As you go from there it should be smooth going! I hope I helped!

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